A375291 - OEIS

%I #8 Aug 10 2024 11:03:21

%S 1,1,1,1,0,-5,-14,-27,-43,-50,-20,91,342,784,1380,1861,1519,-1025,

%T -7877,-21302,-41829,-64128,-70003,-19381,155984,544288,1208731,

%U 2073244,2706380,2003100,-2136215,-12820099,-33219215,-63581579,-94886444,-98351925,-12445158

%N Expansion of (1 - x + x^4)/((1 - x + x^4)^2 + 4*x^5).

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,-2,-2,0,0,-1).

%F a(n) = 2*a(n-1) - a(n-2) - 2*a(n-4) - 2*a(n-5) - a(n-8).

%F a(n) = Sum_{k=0..floor(n/4)} (-1)^k * binomial(2*n-6*k,2*k).

%o (PARI) my(N=40, x='x+O('x^N)); Vec((1-x+x^4)/((1-x+x^4)^2+4*x^5))

%o (PARI) a(n) = sum(k=0, n\4, (-1)^k*binomial(2*n-6*k, 2*k));

%Y Cf. A375289.

%K sign

%O 0,6

%A _Seiichi Manyama_, Aug 10 2024